In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This article for primary teachers suggests ways in which to help children become better at working systematically.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
How many solutions can you find to this sum? Each of the different letters stands for a different number.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
How many different triangles can you make on a circular pegboard that has nine pegs?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
A challenging activity focusing on finding all possible ways of stacking rods.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
A Sudoku with clues given as sums of entries.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
This challenge extends the Plants investigation so now four or more children are involved.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
How many trains can you make which are the same length as Matt's, using rods that are identical?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different triangles on these peg boards, and
find their angles?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Can you find all the different ways of lining up these Cuisenaire
Find out what a "fault-free" rectangle is and try to make some of
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Can you cover the camel with these pieces?